Limited attention. A second motivating example involves constraints arising from Receiver's limited attention span. As Simon ([1]}) noted, “a wealth of information creates a poverty of attention”. Our model enables limiting the signaled information so that it “fits” within Receiver's limited attention.An alternative model of [2]}, [3]} allows Sender to “flood” Receiver with information, but Receiver strategically chooses what to pay attention to.
Constrained persuasion might be viewed as a restriction that simply avoids flooding Receiver with information in expectation (the ex ante model) or always (the ex post model).
Following the rational inattention literature [4]}, define the attention required from Receiver to process Sender's signal \(\sigma \)  as the entropy of the posterior \(p_\sigma \) .[2]} use mutual information of \(p_\sigma \)  and Receiver's perception of it after paying limited attention as the measure of the attention invested by Receiver. In our model, Receiver always pays full attention; thus, the mutual information coincides with the entropy of \(p_\sigma \) .
By constraining the entropy – either in expectation (i.e., ex ante) or of every posterior (i.e., ex post) – we enable Receiver to process the signal despite her limited attention (where the limit is either in expectation or per signal, respectively). A concrete application from [2]} includes a busy executive as Receiver, one of her advisors as Sender and constraints on the signaled information enforced by keeping meetings and briefings short (on average or per meeting).
